It was a dark and stormy night. Private detective Harriet Hesterton had been recruited by her colleague Mahmud Mufti to assist in a case. Some shadowy organization was making counterfeit coins and distributing them to conspiring (or coerced) store owners, who mixed them in with real coins to hide their tracks before giving them as change to customers. Harriet and Mahmud were at what they suspected was one such store.
Two siblings, Janelle and Terrence, are visiting their friends Amy and Sarah. Terrence has just won a game of checkers against Amy for the second time in a row. “Hey Sarah,” Amy said. “This checkerboard reminds me of the magic trick you showed me yesterday.” “Magic trick?” asked Janelle. “The one where you cut up the grid,” Amy prompted her big sister. “Let’s show Terrence and Janelle!” “Okay,” said Sarah, grinning.
In the year 3187, space traveler Alex Ng stops to withdraw some money from her bank account in the standard interplanetary currency. Since extraterrestrials don’t have five fingers, doing business in multiples of one, five, and ten Earth dollars doesn’t really make sense, and neither does doing business in multiples of one, 17, and 68 Yrxiggian knuggyts. Instead, the interplanetary currency is called a blyp, and it comes in multiples of 1, 2, 4, 8, and so on: the powers of 2.
The five crew members of a small pirate ship have just completed a raid in another crew’s territory, and they now have 100 gold coins to split among themselves. “What a raid!” says the captain Anastasia. “Look at the feather in my hat – it’s been torn to shreds.” “Aye,” agrees the first mate Bartholomew. “I have a new hole in my coat.” “Lucky my compass didn’t get smashed while we were retreating back to sea,” remarks the navigator Cornelius.
Paula is re-doing her entryway, and she has decided to inlay a big star-shaped tile into the ceiling. She found a tilework company, Mort’s Tilework, that can cut tile into complex shapes like the one she has in mind: Mort’s Tilework has a seemingly simple pricing scheme for a tile order: $0.25 per square centimeter of area plus $0.10 per centimeter of perimeter. To place her order, Paula needs to send in both a schematic of her shape and her calculations for the area and perimeter of the shape.
Private detective Harriet Hesterton picked up the phone. “Hi Detective Hesterton. This is Gus Spurious,” said the voice on the other side. “Good afternoon. Do you have another suspicious proof to examine?” she replied, remembering their last conversation. “No,” said Gus. “I have a magic trick I can’t figure out. My friend Alina showed it to me and ever since then I’ve been trying to understand how it works.” “Okay,” Harriet told him, picking up a pen.
Leslie Armstrong runs a sporting goods store. Business has been good and the store needs to move to a larger space to accommodate all its customers. Leslie has hire five moving trucks – we can call them Trucks 1 through 5 – to transport all the supplies, and she is now deciding what trucks will carry what supplies. She has 9 identical basketballs in stock on moving day, as well as 61 volleyballs, 88 baseballs, and 323 golf balls.
The town of Isleton, renowned for its widespread decorative woodwork and fine cheeses, spans a cluster of four islands: a. Morton is a tour guide for the town, based on the east side of the south island (in the blue building). He advertises to tourists that his walking tour crosses every bridge in the city. To minimize the amount of walking on the tour, Morton decides he’d like to plan the tour’s path so it crosses each bridge exactly once, ideally starting and ending at the same location.
Two sisters, Amy and Sarah, are staying busy on a long car ride. Sarah is reading a book. Amy is poking her older sister and trying to start a conversation. To give Amy something to do, Sarah looks up from her book and says, “Look – I’ll give you a math puzzle, and once you get the answer, I’ll put down the book and talk with you.” Amy is up for the challenge and agrees.
Suppose we have a triangle, and suppose we also draw its altitudes (that is, the heights if we treat each side length as the base): If the three side lengths and the three altitudes are all integers AND they’re all different from each other, is it ever possible for four of the six numbers to be prime? Nicki and Dave disagree what the answer should be: Dave thinks it should be possible, while Nicki thinks it’s probably impossible.